Multi-scale and multi-criteria mapping of mountain peaks as fuzzy entities

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. Mountain peaks are mapped as multi-scale entities with modifiable boundaries and variable contents. Four semantic meanings are imported and quantified to first characterize peaks at a range of spatial scales and then evaluate the multi-criteria 'peakness' at each scale. Peakness is defined as the prototypicality of identified summits and as the similarity of each point (cell) to summits. The procedure then summarizes the individual-scale peakness across considered spatial scales into a univariate membership surface. This allows mapping of vague peak entities as non-homogeneous peak regions whose boundaries depend on user-specified peakness thresholds. This procedure was applied in a case study to tackle several challenges in landform delineation, including boundary, spatial continuity, spatial scale, topographic context, and multi-criteria definition.